Whence the Uniformity PrincipleJohn P. McCaskey · Stanford University

Richard Whately

AncientScholastic

Humanist

Whatelian

Prosecuting a wrongdoer, even if it’s your own father.

What is piety?

That’s an example. What is piety itself? Doing what pleases the

gods.But gods disagree.

And there are many kinds of disagreement:Disagreement over which number is greater.Disagreement over which thing is larger.Disagreement over which thing is heavier.Disagreement over just and unjust.

Disagreement over beautiful and ugly.

Disagreement over good and bad.Piety is what pleases all gods.But is it pious because it

pleases the gods or does it please the gods because it is pious?

What is loved vs. what loves.

What is the difference?

What is led vs. what leads.

What is seen vs. what sees.So . . . what is admired vs. what admires.

I don’t know which.Let’s start over. Isn’t everything pious also just but not vice versa?

Yes.

Then piety is a kind of justice. What kind?

Ancient“

”Two things may be fairly ascribed to Socrates: inductive reasoning and universal definition.

Ancient

• Ensure property applies in individual cases.

• Test kinds broader and narrower.• Identify linked contraries.• Ensure the predicate can be applied

broadly.• Use terms that are unambiguous.• Identify temporal qualifications.• Identify dependencies.• Use language that makes clear in what

way exceptions are allowed.• Check relationship of whole to parts.• Be clear whether relationship is absolute

or relative.• . . .

Use observations and comparisons to . . .

“”

Two things may be fairly ascribed to Socrates: inductive reasoning and universal definition.

Ancient

“This procedure, which arrives at its aim from several instances, may be named inductio, which in Greek is called epagoge; Socrates made extensive use of it in his discussions.”

— Topica

“”

Two things may be fairly ascribed to Socrates: inductive reasoning and universal definition.

“[used] chiefly by Socrates and his disciples,”

— De InventionePhoto posted on Flickr by John Sellars (aka

photobiblon)

Scholastic

BoethiusPeter

AlbertAquinas

ScotusOckham

Zabarella

al-FarabiAvicenna

AverroesAncient

ClementAlexander

Sextus EmpiricusThemistius

Ammonius HermiaeSimplicius

Philoponus

Father, Son and Holy Spirit are eternal.[God is Father, Son and Holy Spirit.]

Therefore, God is eternal.

An induction has no necessity unless turned into a syllogism.

Everything that is this man, or that man, et cetera, is an animal.[Every man is this man, or that man, et cetera.]

Therefore, every man is an animal.

An induction is a syllogism in Barbara

with the minor premise

suppressed.

AncientScholastic

Socratic

Higginsian

Ancient

Humanist

Scholastic

Thomas

Wilson

1551

1552

Ancient

Humanist

Sunlight

Sunlight through magnifier

Flame

Heated or boiling liquidsWet, compressed plantsFibrous fabricsQuicklime with waterAnimals

Horse dung

LightningMeteors

Volcanoes

Solids on fireNatural hot baths

Distilled spirits?

PresenceRelated Absence

MoonlightStarlight…magnifier turned around?Moonlt through magnifier?

Liquids in natural state“further inquiry is needed”“let an experiment be made”Quicklime with oil?Insects

Sheet lightningComets, aurora borealis

Rotting wood?“not enough investigations”

X

X

Degrees

Fish

Different parts of animals

Dung as fertilizer

Kinds of animals

Corpse right after death

SeasonsAltitude

Lightning hotter than fireMany kindsSmaller solids heat up faster

Three Tables

1• Light? No: Dark things can be hot.• Something celestial? No: Heat can emerge from

underground.• Something terrestrial? No: Heat can come from the

heavens.• Expansion? No: Water does, but iron doesn’t expand when

heated.• Rarity? No: Fire and hot air are rare, but dense things can

be hot.• Motion? Not motion generally; some things move without

getting hot, but everything hot involves motion.

Candidates&

Exclusions

2

Heat is a kind of motion.3 Genus

• Expansive motion—most apparent in flame, but also apparent in boiling liquids, combustible materials, metals melting, rocks softening when heated. Also consistent with opposite behavior in cold. For example, glass expands when heated then contracts and cracks when cooled.

• Motion is of the parts (maybe too small to see) not of the whole as a unit . . .

4 Differentia

Definition5 Heat is an expansive motion which is checked

and restrained, and acting through particles, expanding in all directions, . . .

. . . a true induction

Scholastic

Socratic

Scholastic

Exploding French gunpowder is hot.Exploding German gunpowder is hot.Exploding English gunpowder is hot.

All exploding gunpowder is hot.

Heat is such-and-such motion.

All gunpowder has heat.

By induction

By the nature of definition

Hot things exhibit such-and-such motion.

Such-and-such motion is heat.All gunpowder has such-and-such motion.

Humanist

Socratic

Ancient

Ancient

2Identify Genus : the (Fundamental) Idea

1Identify Facts

“Induction is a term applied to describe the process of a true Colligation of Facts by means of an exact and appropriate Conception.”The “Inductive Step” is the “Invention of the Conception.” “In every inference by Induction, there is some Conception superinduced upon the Facts.”

Scholastic

3Form Conception4Form Definition

Humanist

Socratic William Whewe

ll

AncientScholastic

“Inductive Principle”

Things will continue as they have.

The very foundation of induction.

But the principle is not true.

?

Humanist

Socratic

Thomas Reid

(But induction is valid.)

AncientScholastic

Whatelian

Socratic

Higginsian

Humanist

Ancient

Humanist

This, that and the other magnet attract iron.[All magnets are this, that and the other.]

Therefore, all magnets attract iron.

An induction is a syllogism in Barbara

with the minor premise

suppressed.

1823

* Not the minor, as Aldrich represents it.

1826

Scholastic

* “Not the minor, as Aldrich represents it.”

“[Induction is] a Syllogism in Barbara

with the major* Premiss suppressed.”

Henry Aldrich

Richard Whately

Not the minor, as Aldrich represents it. The instance he gives will sufficiently prove this: . . . “All magnets are this, that and the other”. . . is manifestly false.

Therefore all magnets attract iron.

Observed tyrannies are short-lived.

Therefore Socrates is mortal.

Therefore all tyrannies are short-lived.

Therefore attracting iron is a property of all magnets.

Therefore being short-lived is a property of all tyrannies.

Being short-lived is a property of observed tyrannies.

[A property of observed tyranniesis a property of all tyrannies.]

“[Induction is] a Syllogism in Barbara

with the major* Premiss suppressed.”

Minor Major

Minor

Conc.

Major

Observed tyrannies are short-lived.

Therefore all tyrannies are short-lived.

Therefore being short-lived is a property of all tyrannies.

Being short-lived is a property of observed tyrannies.

[A property of observed tyranniesis a property of all tyrannies.]

Minor

Conc.

Major

“[Induction is] a Syllogism in Barbara

with the major* Premiss suppressed.”

“original”“extremely important”

“[This] one remark would have sufficed to correct the erroneous notion the ancients had of induction, and to which Lord Bacon . . . [was responding]. They in fact mistook altogether the inductive syllogism, completing it by the addition of a minor, instead of a major.”

1828

“palpably suicidal”

“As Archbishop Whately remarks, every induction is a syllogism with the major premise suppressed; or (as I prefer expressing it) every induction may be thrown into the form of a syllogism by supplying a major premise. If this be actually done, the principle we are now considering, that of the uniformity of the course of nature, will appear as the ultimate major premise of all inductions.”

“[Induction is] a Syllogism in Barbara

with the major* Premiss suppressed.”

Socratic

Higginsian

Propositional

Inference

Concept-Formation

Prior AnComment’

rsTopicsCicero

Early Humanist

s

? ?

Bacon Purge thisFind formal causeü

û

Better sense: Syllogism with supp’d major

Original and strict

sense

üWhately ’23

Mill ’43Syllogism

w. uniformity principle

Mere descriptionû ü

Ancients What is piety?

ScholasticsSyllogism

by complete

enumeration

Whewell

Each induction

ends with a new

conception

De Morgan ’47Original and logical sense

The sense nowadays

CorrectIncorrectû ü Bain ’70

Find probability

that the major is true

Jevons ’70

• Induction is about universal propositions, not universal concepts.

• It’s a risky kind of inference to be understood with reference to the better kind, deduction.• Uniformity principle is

a presumed major premise.• Logicians and mathe-

maticians have displaced philosophers of mind.

• It’s about propositional inference not abstraction.

“In an Induction, there are three essentials:—(1) the result must be a proposition as opposed to a notion. . . . Sometimes we are liable to confound the two. Definitions, or general notions, are limited to one indivisible fact or attribute; they are contrasted with inductions, which always join at least two facts or attributes . . . . The generalized notions of . . . resistance, whiteness, heat could not be confounded with inductions.” Logic, Book III, “Induction”

Socratic

Propositional

Inference

Concept-Formation

Better sense: Syllogism with supp’d major

Original and strict

sense

üWhately ’23

Mill ’43Syllogism

w. uniformity principle

Mere descriptionû ü

De Morgan ’47Original and logical sense

The sense nowadays

CorrectIncorrectû ü

Bain ’70Find

probability that the major is true

Jevons ’70

“ Why is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, . . . go such a very little way towards establishing an universal proposition? Whoever can answer this question . . . has solved the problem of Induction. ”

“ Note 2.—Since the time of Hume, the nature of our conception of Cause has formed one of the principal topics of philosophical controversy. . . . (a controversy, however, which possesses a historical rather than a practical or scientific interest). ”

Fowler ’70Presumptions in any inference: · Sense perception · Memory · Uniformity of natureVarious defenses: · Mill’s · Reid’s · Hume’s · Venn’s own

Venn ’89

“ The very concept of an experimental inference involves a great petitio principii. Induction owes all its force to the premise that the future will be like the past, which is just what the induction itself seeks to infer. ” “— as Hume relentlessly insisted —”

Cassirer ’05

Keynes ’21

“ Hume’s sceptical criticisms

are usually associated with

causality; but argument by

induction . . .

was the real object of his

attack. . . . Hume’s statement

of the case against induction

has never been improved

upon. ”

HigginsianHumean

AncientScholastic

Socratic

Higginsian

Humanist

Whatelian

“[Logic] is the grammar of reasoning by means of words.”

“[Logic] is the art of employing language properly.”

“In introducing the mention of language . . . to the definition of Logic, I have departed from established practice, in order that it may be clearly understood, that Logic is entirely conversant about language.”

Whence the Uniformity PrincipleJohn P. McCaskey · Stanford University